Movement equations 3 : surrounding area of the solid, fundamental principle of dynamics, energy equations / Michel Borel, Georges Vénizélos.

Format:

Book

Author/Creator:

Borel, Michel, author.

Vénizélos, Georges, author.

Series:

Non-deformable solid mechanics set ; volume 3.

Mechanical Engineering and Solid Mechanics Series. Non-deformable Solid Mechanics Set ; Volume 3

Language:

English

Subjects (All):

Solids.

Solid state physics.

Physical Description:

1 online resource (1 volume) : illustrations.

Edition:

1st edition

Other Title:

Movement equations three

Place of Publication:

London, England ; Hoboken, New Jersey : Wiley : iSTE, 2017.

System Details:

text file

Summary:

This volume is the focal point of the work undertaken in the previous volumes of this set of books: the statement of the fundamental principle of the dynamics whose implementation, according to two paths whose choice depends on the problem to be treated, leads to equations of motion. In order to achieve this, it is treated first of all in the context of solids in their environment, as a prerequisite for the formulation of the fundamental principle. Then, in addition to its use in some exercises, the approach is illustrated by three particular cases. The first is an example where it is developed end-to-end and addresses the two approaches that lead to the equations of motion. The two other examples deal with two classical but important subjects, the movement of the Earth according to the hypotheses that can be stated about it, and Foucault’s pendulum.

Contents:

Cover

Half-Title Page

Title Page

Copyright Page

Contents

Introduction

Table of Notations

1. Fundamental Principle of Dynamics

1.1. The fundamental principle of dynamics and its scalar consequences

1.1.1. Fundamental principle of dynamics

1.1.2. Choosing a frame

1.1.3. Preferred time scale

1.2. Secondary principles

1.2.1. First secondary principle of the separation of effects

1.2.2. Second secondary principle of effort generators

1.2.3. Third secondary principle of effort receivers

1.3. Motion of a set ( D ) in a given frame &lt

λ &gt

1.3.1. Presentation of the context

1.3.2. Combination of accelerations

1.3.3. Coriolis inertial torsor

1.3.4. Drive inertial torsor

1.3.5. Relation between the dynamic torsors in the two frames

1.3.6. Applying the fundamental principle

1.4. Motion of a non-deformable solid in a given frame

1.4.1. Coriolis inertial torsor

1.4.2. Drive inertial torsor

2. Solid in Space. Efforts and Links: Power

2.1. Degrees of freedom of a solid

2.2. Free solid

2.2.1. Velocity distributing torsor

2.2.2. Kinetic torsor

2.2.3. Dynamic torsor

2.2.4. Kinetic energy

2.2.5. Applying the fundamental principle of dynamics

2.3. Linked solids and links

2.3.1. Links

2.3.2. Configurable links

2.3.3. Linked solids

2.4. Virtual power developed on a material set ( D )

2.5. Power of the efforts exerted on a solid

2.5.1. Definition

2.5.2. Discrete force field

2.5.3. Non-deformable mechanical set

2.5.4. Continuous mechanical set

2.6. Properties of power

2.6.1. Powers developed in two distinct frames

2.6.2. Case of a system of forces equivalent to zero acting on a solid

2.6.3. Case of a system of forces equivalent to zero acting on a deformable mechanical set

2.6.4. Partial powers.

3. Scalar Consequences and Movement Equations

3.1. Establishment principle of the movement equations

3.1.1. Vector projection

3.1.2. Torsor products

3.1.3. Choice of representative scalar consequences

3.2. Movement equations of a solid

3.2.1. Scalar consequences via vector projection

3.2.2. Scalar consequences of the analytic mechanics of motion

3.2.3. Linear independence of torsors

3.2.4. Exercise 3 - Scalar consequences using analytical mechanics

3.3. Movement equations of the free solid

3.4. Movement equations of the linked solid with configurable links

3.4.1. Velocity distributing torsor and partial distributing torsors

3.4.2. Case of configurable links independent of time

3.4.3. Case of configurable links dependent on time

3.4.4. Perfect configurable links

3.5. Energetic expression of the equations of analytical mechanics

3.5.1. Case of configurable links explicitly independent of time

3.5.2. Case of configurable links explicitly dependent on time

3.6. Summary example

3.6.1. Locating the solid

3.6.2. Links

3.6.3. Solid kinematics

3.6.4. Kinetics of the solid

4. Particular Applications

4.1. Simulation of the motion of Earth

4.1.1. Application of the fundamental principle

4.1.2. Theorem of dynamic moment at G

4.1.3. Theorem of dynamic resultant

4.2. Foucault's pendulum

4.2.1. Observation of the phenomenon

4.2.2. Analyzing the phenomenon

5. Methodological Formulary

5.1. Reference outline on the motion of a solid

5.1.1. Representation of a frame

5.1.2. Reference frame

5.1.3. Situation of the Solid

5.1.4. Notion of basis in a frame

5.2. Kinematics of the Solid

5.2.1. Kinematics of a material point M

5.2.2. Kinematics of non-deformable solids

5.3. Principle of motion with fixed plane

5.3.1. Kinematics of a Solid.

5.3.2. Fixed and mobile centroids in a motion with fixed plane

5.4. Combination of motions

5.4.1. Combination of velocities

5.4.2. Combination of accelerations

5.5. Kinetics of non-deformable solids

5.5.1. Center of measure

5.5.2. Linear momentum and kinetic torsor

5.5.3. Dynamic torsor

5.5.4. Kinetic energy

Bibliography

Index

Other titles from iSTE in Mechanical Engineering and Solid Mechanics

EULA.

Notes:

Includes bibliographical references and index.

Description based on print version record.

ISBN:

9781119467083

111946708X

9781119467038

1119467039

9781119467090

1119467098

OCLC:

1031484909